Step-by-step solutions on video for all chapter test exercises from the text These are two different ways of showing the solution set of the inequality. English and Spanish Subtitles Available CHAPTER TEST PREP VIDEOS ARE ACCESSIBLE THROUGH THE FOLLOWING: A Library of Functions ConstantFunction LinearFunction Linear Function AbsoluteValueFunction y(cid:2)b y(cid:2)mx(cid:5)b,m(cid:4) 0 y(cid:2)mx(cid:5)b,m(cid:3) 0 y(cid:2)(cid:3)x(cid:3) 5 (cid:6)5 5 (cid:6)1 SquaringFunction SquareRootFunction CubingFunction CubeRootFunction y(cid:2)x2 y(cid:2)(cid:2)x y(cid:2)x3 y(cid:2)(cid:2)3x 5 4 6 3 (cid:6)3 3 (cid:6)6 6 (cid:6)3 3 (cid:6)3 6 (cid:6)2 (cid:6)2 (cid:6)6 (cid:6)3 Quadratic Function Quadratic Function Rational Function Rational Function y(cid:2)ax2(cid:5)bx(cid:5)c,a(cid:4) 0 y(cid:2)ax2(cid:5)bx(cid:5)c,a(cid:3) 0 y(cid:2)a,a(cid:4) 0 y(cid:2)a,a(cid:3) 0 x x Exponential Function Exponential Function Logarithmic Function Logarithmic Function y(cid:2)ax, a(cid:4) 1 y(cid:2)ax, 0 (cid:3)a(cid:3) 1 y(cid:2) logbx,b(cid:4) 1 y(cid:2) logbx, 0 (cid:3)b(cid:3) 1 Intermediate Algebra ELEVENTH EDITION Marvin L. Bittinger Indiana University Purdue University Indianapolis Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Editorial Director Christine Hoag Editor in Chief Maureen O’Connor NOTICE: Executive Editor Cathy Cantin This work is Executive Project Manager Kari Heen protected by U.S. copyright laws and Associate Editors Joanna Doxey and is provided solely for Christine Whitlock the use of college Editorial Assistant Jonathan Wooding instructors in review- Production Manager Ron Hampton ing course materials for classroom use. Composition Pre-Press PMG Dissemination or sale Editorial and Production Services Martha K. 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All recipi- Senior Media Buyer Ginny Michaud ents of this workare Text Designer Geri Davis/The Davis Group, Inc. expected to abide by Senior Designer/Cover Design Beth Paquin these restrictions Cover Photograph © Jim Wehtje and to honor the intended pedagogical purposes and the Photo Credits needs of other Photo credits appear on p. 838. instructors who rely on these materials. Library of Congress Cataloging-in-Publication Data Bittinger, Marvin L. Intermediate algebra. — 11th ed. / by Marvin L. Bittinger. p. cm. Includes index. 1. Algebra—Textbooks. I. Bittinger, Marvin L. Intermediate algebra. II. Title. QA154.3.B578 2011 512.9—dc22 2009021865 Copyright © 2011 Pearson Education, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, record- ing, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. 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Addison-Wesley is an imprint of ISBN-13:978-0-321-61336-3 www.pearsonhighered.com ISBN-10:0-321-61336-8 Contents Index of Applications vii 1.4 Sets, Inequalities, and Interval Notation 113 Author’s Note to Students xi TRANSLATING FOR SUCCESS 122 Preface xii 1.5 Intersections, Unions, and Compound Inequalities 129 R 1.6 Absolute-Value Equations Review of Basic Algebra 1 and Inequalities 141 SUMMARY AND REVIEW 152 Part 1 Operations TEST 157 R.1 The Set of Real Numbers 2 R.2 Operations with Real Numbers 12 R.3 Exponential Notation and Order of 2 Graphs, Functions, Operations 23 and Applications 159 Part 2 Manipulations R.4 Introduction to Algebraic Expressions 32 2.1 Graphs of Equations 160 R.5 Equivalent Algebraic Expressions 38 2.2 Functions and Graphs 174 R.6 Simplifying Algebraic Expressions 46 2.3 Finding Domain and Range 188 R.7 Properties of Exponents and Scientific MID-CHAPTER REVIEW 193 Notation 54 2.4 Linear Functions: Graphs and Slope 195 SUMMARY AND REVIEW 66 2.5 More on Graphing Linear Equations 206 TEST 71 VISUALIZING FOR SUCCESS 213 2.6 Finding Equations of Lines; 1 Solving Linear Equations Applications 218 and Inequalities 73 SUMMARY AND REVIEW 229 TEST 238 1.1 Solving Equations 74 CUMULATIVE REVIEW: CHAPTERS 1–2 241 1.2 Formulas and Applications 88 1.3 Applications and Problem Solving 97 MID-CHAPTER REVIEW 111 iii 4.7 Factoring: A General Strategy 382 3 Systems of Equations 243 4.8 Applications of Polynomial Equations and Functions 387 TRANSLATING FOR SUCCESS 395 3.1 Systems of Equations in Two Variables 244 SUMMARY AND REVIEW 401 3.2 Solving by Substitution 253 TEST 407 3.3 Solving by Elimination 259 CUMULATIVE REVIEW: CHAPTERS 1–4 409 3.4 Solving Applied Problems: Two Equations 268 Rational Expressions, TRANSLATING FOR SUCCESS 277 5 Equations, and MID-CHAPTER REVIEW 282 Functions 411 3.5 Systems of Equations in Three Variables 284 5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying 412 3.6 Solving Applied Problems: Three Equations 291 5.2 LCMs, LCDs, Addition, and Subtraction 424 3.7 Systems of Inequalities in Two Variables 299 5.3 Division of Polynomials 435 5.4 Complex Rational Expressions 443 VISUALIZING FOR SUCCESS 308 MID-CHAPTER REVIEW 450 SUMMARY AND REVIEW 313 5.5 Solving Rational Equations 452 TEST 319 5.6 Applications and Proportions 460 CUMULATIVE REVIEW: CHAPTERS 1–3 321 TRANSLATING FOR SUCCESS 468 5.7 Formulas and Applications 474 4 Polynomials and 5.8 Variation and Applications 478 Polynomial Functions 323 SUMMARY AND REVIEW 489 4.1 Introduction to Polynomials and TEST 495 PolynomialFunctions 324 CUMULATIVE REVIEW: CHAPTERS 1–5 497 4.2 Multiplication of Polynomials 336 4.3 Introduction to Factoring 347 Radical Expressions, 6 4.4 Factoring Trinomials: x2 + bx + c 354 Equations, and Functions 499 MID-CHAPTER REVIEW 360 4.5 Factoring Trinomials: 6.1 Radical Expressions and Functions 500 ax2 + bx + c, a Z 1 362 6.2 Rational Numbers as Exponents 511 4.6 Special Factoring 370 6.3 Simplifying Radical Expressions 518 VISUALIZING FOR SUCCESS 377 iv Contents 6.4 Addition, Subtraction, and More 8 Exponential and Multiplication 527 Logarithmic Functions 671 MID-CHAPTER REVIEW 533 6.5 More on Division of Radical 8.1 Exponential Functions 672 Expressions 535 8.2 Inverse Functions and Composite 6.6 Solving Radical Equations 540 Functions 686 6.7 Applications Involving Powers 8.3 Logarithmic Functions 703 and Roots 551 8.4 Properties of Logarithmic Functions 714 TRANSLATING FOR SUCCESS 553 MID-CHAPTER REVIEW 720 6.8 The Complex Numbers 558 8.5 Natural Logarithmic Functions 722 SUMMARY AND REVIEW 569 VISUALIZING FOR SUCCESS 727 TEST 575 8.6 Solving Exponential and CUMULATIVE REVIEW: CHAPTERS 1–6 577 Logarithmic Equations 731 8.7 Mathematical Modeling with Exponential and Logarithmic Functions 738 7 Quadratic Equations TRANSLATING FOR SUCCESS 746 and Functions 579 SUMMARY AND REVIEW 752 7.1 The Basics of Solving Quadratic TEST 760 Equations 580 CUMULATIVE REVIEW: CHAPTERS 1–8 763 7.2 The Quadratic Formula 594 7.3 Applications Involving 9 Quadratic Equations 601 Conic Sections 765 TRANSLATING FOR SUCCESS 607 7.4 More on Quadratic Equations 613 9.1 Parabolas and Circles 766 MID-CHAPTER REVIEW 622 9.2 Ellipses 779 7.5 Graphing f x (cid:2) a x (cid:4) h 2 (cid:3) k 624 MID-CHAPTER REVIEW 787 7.6 Graphing f x (cid:2) ax2 (cid:3) bx (cid:3) c 633 1 2 1 2 9.3 Hyperbolas 789 VISUALIZING FOR SUCCESS 638 1 2 VISUALIZING FOR SUCCESS 793 7.7 Mathematical Modeling with Quadratic 9.4 Nonlinear Systems of Equations 797 Functions 642 7.8 Polynomial Inequalities and Rational SUMMARY AND REVIEW 807 Inequalities 653 TEST 813 SUMMARY AND REVIEW 661 CUMULATIVE REVIEW: CHAPTERS 1–9 815 TEST 667 CUMULATIVE REVIEW: CHAPTERS 1–7 669 Contents v Appendixes Photo Credits 838 Answers A-1 A Handling Dimension Symbols 822 Glossary G-1 B Determinants and Cramer’s Rule 825 Index I-1 C Elimination Using Matrices 830 D The Algebra of Functions 835 vi Contents Index of Applications Agriculture Growth of bacteria, 685, 759 Ticket profits, 648 Blending flower seeds, 270–271 Insect-eating lizard, 64 Total cost, 332, 352 Bordered garden, 642–643 Mass of an electron, 64 Total profit, 332, 660 Composting, 650 Mass of water in body, 485 Total revenue, 332, 352 Corral design, 649 Sound of cicadas, 747 Video game sales, 407 Farm income, 32–33 Wild horse population, 410, 464–465 Volume of mail, 203 Feed lot, 608 Wildlife populations, 470 Fenced-in land, 643 Chemistry Filling a grain bin, 578 Business Acid mixtures, 763 Garden design, 650, 805 Artist’s prints, 103 Ammonia solutions, 819 Grain flow, 746 Book club, 818 Carbon dating, 744–745, 749, 759, Harvesting time, 578 Break-even point, 806 762, 819 Livestock feed, 278 Catering, 278 Half-life, 750 Mixing fertilizers, 272–274 Changing marketing strategies, 100–101 Ink remover, 278 Vegetable garden, 555, 812 Chicken dinner sales, 319 Mixing solutions, 274, 283, 319, 322, Chocolate making, 763 395, 621 Astronomy Copy budget, 157 Nontoxic floor wax, 278 Alpha Centauri, 65 Delivering leaflets, 550 Orange drink mixtures, 317 Brightest star in the sky, 65 Delivery service, 126 pH of liquids, 739, 740, 747 Distance from the earth to the sun, 59 Dry cleaners, 279 pH of tomatoes, 762 Distance from the sun to the planet Falling DVD sales, 112 Temperatures of liquids, 139 Saturn, 58 Filling sandbags, 411, 460–461 Temperatures of solids, 127 Light from the sun to a planet, 60 Food and drink sales, 816 Lunar eclipses, 474–475 Haircutting, 203 Construction Mass of Jupiter, 60 Homespun Jellies, 237 Architecture, 255–256, 649, 670, 801–802 Mass of Pluto, 72 Inventory, 322 Beam weight, 486 Mass of the sun, 60 iPod sales, 746 Box construction, 609 Orbit ofVenus, 64 Laptop and desktop computer sales, 108 Carpentry, 394 Planetary orbit, 783 Lens production, 297 Clearing a lot, 469 Satellite’s escape velocity, 477 Manufacturing, 151 Covered bridges, 750 Weight of an astronaut, 487 Maximizing profit, 650 Cross section of a roof, 98 Weight on Mars, 471, 485 Minimizing cost, 649 Cutting a board, 102 Weight on the moon, 471 Newspaper circulation, 203 Doorway construction, 778 Newspaper delivery, 470 Fencing, 122 Automotive Office expense, 277 Footer of a house, 552 Auto dealers, 228 Organic food sales, 748 Grade of a stairway, 205 Automobile pricing, 295 Patents issued, 108 Home construction, 750 Automotive maintenance, 279, 281 PDQ shopping network, 468 Installing seamless guttering, 102 Automotive repair, 573 Pizza sales, 73, 112, 395 Jackhammer noise, 747 Daytime accidents, 651 Placing wrappers on canned goods, 470 Ladder location, 398, 408, 602, 603 Fuel economy, 281 Printing and engraving, 65 Lot dimensions, 242 Gas mileage, 463, 473 Printing tee shirts, 469 Molding plastics, 649 Horsepower of an engine, 96 Producing bearings, 409 Painting, 469, 470, 493, 550, 557 Median age of cars, 238 Radio advertising, 242, 322 Patio design, 649 Models of Indy Cars, 470 Railing sales, 806 Pitch of a roof, 204 Nighttime accidents, 651 Retail pricing, 106 Plank height, 553 Stopping distance of a car, 487 Retail sales, 269, 278 Plumbing, 556, 750 Retail trade, 224–225 Predicting paint needs, 496 Biology Sales promotion, 267 Retaining wall, 471 Bees and honey, 480 Sales, 646 Road grade, 202 Diameter of a helium atom, 58 Shipping, 485 Roofing, 557 Fish population, 468 Telemarketing, 295 Room dimensions, 157 vii